... knowing if Trump would still have won had the story come out.
if = whether, 引导宾语从句。该宾语从句本身又是一个带有条件状语从句的虚拟条件句，had the story come out = if the story had come out.
当宾语从句为一般问句时，用whether或者if引导宾语从句，而不用that。所以不存在省略that的问题。
Would Trump still have won had the story come out？
= Would Trump still have won if the story had come out？
这个问句要做knowing的宾语，首先要把它改为名词性从句，即用whether或if引导，去倒装、去问号，则得到：
...knowing whether/if Trump would still have won had the story come out.
= ... knowing whether/if Trump would still have won if the story had come out.
